Math, asked by Akku1178, 1 year ago

If the ratio of the roots of the equation 4x^(2)-6x+p=0 is 1:2 then the value of p is​

Attachments:

Answers

Answered by rajamallickraja19
6

4×^2-6x+p=0

if x=1/2

then 4^2-6×1/2+p=0

16-3+p=0

13+p=0

p= -13

Answered by smithasijotsl
9

Answer:

The value of 'p' = 2

Step-by-step explanation:

Given

The quadratic equation is 4x²-6x+p=0

The ratio of the roots of the equation = 1:2

To find,

The value of 'p'

Recall the formula,

If α and β are the roots of the quadratic equation ax² + bx +c = 0, then

α + β = \frac{-b}{a} and αβ = \frac{c}{a}

Solution:

Since the roots of the quadratic equation are in the ratio 1:2, let the take the roots as 'k' and '2k'

Comparing the given equation with  ax² + bx +c = 0, we get

a = 4, b = -6 and c =  p

Since the roots are k and 2k we have, α = k and β = 2k

α + β = \frac{-b}{a} ⇒k+2k = \frac{-(-6)}{4}

⇒3k = \frac{6}{4}  = \frac{3}{2}

k = \frac{1}{2}

Also we have,

αβ = \frac{c}{a} ⇒k×2k = \frac{p}{4}

2k²= \frac{p}{4}

Substitute the value of k = \frac{1}{2} we get,

2( \frac{1}{2})² =  \frac{p}{4}

\frac{1}{4}  =  \frac{p}{4}

p = 2

∴ The value of 'p' = 2

#SPJ2

Similar questions